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Reptile [31]
3 years ago
8

Ken has a pole that is 26 inches long. He wishes to cut it into two pieces so that one piece will be 8 inches longer than the ot

her. How long must the shorter piece be?
Mathematics
1 answer:
Yuliya22 [10]3 years ago
3 0

Answer:

9 inches

Step-by-step explanation:

Do the question algebraically, represented by this equation:

let x be the shorter piece

x + (x + 8) = 26                      (longer piece is 8 units longer)

Remove brackets

x + x + 8 = 26                 Combine like terms              

2x + 8 = 26                   Start isolating "x"

2x + 8 - 8 = 26 - 8           Subtract 8 from both sides

2x = 18

2x/2 = 18/2           Divide both sides by 2

x = 9                    shorter piece

The shorter piece would be 9 inches.

If you needed the longer piece too:

longer piece = x + 8

x + 8

= 9 + 8

= 17

The longer piece would be 17 inches.

Check your answer:

Longer + Shorter = 26           Substitute the lengths

17 + 9 = 26                    Add

26 = 26                same number

LS = RS                left side equals right side

The answer is correct.

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To solve this we are going to use the exponential function: f(t)=a(1(+/-)b)^t
where
f(t) is the final amount after t years
a is the initial amount
b is the decay  or grow rate rate in decimal form
t is the time in years

Expression A 
f(t)=624(0.95)^{4t}
Since the base (0.95) is less than one, we have a decay rate here.
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b=|1-0.95|*100%
b=0.05*100%
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We can conclude that expression A decays at a rate of 5% every three months.

Now, to find the initial value of the function, we are going to evaluate the function at t=0
f(t)=624(0.95)^{4t}
f(0)=624(0.95)^{0t}
f(0)=624(0.95)^{0}
f(0)=624(1)
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Expression B
f(t)=725(1.12)^{3t}
Since the base (1.12) is greater than 1, we have a growth rate here.
To find the rate, we are going to use the same equation as before:
b=|1-base|*100%
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b=0.12*100%
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We can conclude that expression B grows at a rate of 12% every 4 months.

Just like before, to find the initial value of the expression, we are going to evaluate it at t=0
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f(0)=725(1.12)^{0t}
f(0)=725(1.12)^{0}
f(0)=725(1)
f(0)=725
The initial value of expression B is 725.

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- Expression A has an initial value of 624, while expression B has an initial value of 725.

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